3-rd Workshop3-rd Workshop of of WOMEN WOMEN ProjectProjectRome January 19-th, 2007

University of Rome “Sapienza”, INFOCOM Dept. (Faculty of Engineering)

Wireless Mesh Networks:Wireless Mesh Networks:

First part:First part:

Point to point links ofPoint to point links ofwireless mesh nodes based on wireless mesh nodes based on

MIMO UWB-IR technologyMIMO UWB-IR technology

Outline

System model: main characteristics

Performance of the MIMO UWB-IR Co-Decoder

Derivation of the MIMO UWB-IR Co-Decoder

Conclusions

Main aspects of the MIMO UWB-IR Synchronizer

NON-COHERENT NON-COHERENT ML ML

SYNCHRONIZERSYNCHRONIZER

PILOT SIGNALPILOT SIGNAL GENERATOR GENERATOR

FORFOR SYNCHRONISMSYNCHRONISM

RECOVERYRECOVERY

MIMO UWB-IR System Model(with Poisson distributed multipath fading)

1(1)

0

( ) ( )SN

pilot S Wm

x t E s t mT

0, . . .[ ]V

1( )

0

( ) / ( )fN

idata f t f i p

m

UWB IR M OPPM data signal

x t E N p t mT d T

1 0

( ) (( , ) )( )tN

j ji

data signal measured at j thantenna

n

V

n in

h j iy t x w tt

ji0

r t

( ) ( j,i) ( ) ,

1 j N , 1 i N

V

n nn

h t h t

1

rN

j

tN

111( )h t

rN 1( )h t

j1( )h t

t1N ( )h t

r tN N ( )h t

ji0

r t

( ) ( j,i) ( ) ,

1 j N , 1 i N

V

n nn

h t h t

(1)

0

( ,( ) ( ) ( )) j

data signal measured at

j pilo

j t

V

n

han

n

t a

t

en

n

n

h j ir t x t w t

SPACE-TIME CODED SPACE-TIME CODED PACKET TRANSMITTERPACKET TRANSMITTER

ADOPTING OPPMADOPTING OPPMMODULATION FORMAT MODULATION FORMAT

NON-COHERENT NON-COHERENT ML ML

DECODERDECODER

The MIMO UWB-IR channel model

11 21 1

21 22 2

1 2

( ) ( ) ...... ( )

( ) ( ) ...... ( )

( ) ......................................

......................................

( ) ( )...... ( )

r

r

t t t r

N

N

N N N N

h t h t h t

h t h t h t

t

h t h t h t

H t rX ( MIMO UWB-IR (N N )

channel responses matrix)

.

K.Yu, B.Ottersten, "Models for MIMO propagation channels : a review",

Wireless Communication and Mobile Computing, vol.2, pp. 653 - 666, 2002

, , , t r0 0

( ) ( , ) ( , ) ( ), 1 i N , 1 j NQ N

ji q n q n q q nq n

h t b j i j i t T

Multiple Cluster SISO channel responses with Poisson distributed arrivals and clusters and Log-Normally distributed path gains. ( It has been adopted for describing different indoor and outdoor propagation environments)

A. Molish, D. Cassioli, et alii, “A Comprehensive Standardized Models for UltraWideband Propagation Channels”, IEEE Tr. On antennas and Propagation, Vol.54, No.11, pp.3151-3166, Nov.2006.

UWB-IR channel models

SISO

UWB-IR

channel Cluster mean frequency

Ray mean frequency

Cluster decay factor

Ray decay factor

Multipath Spread

CM 1

(LOS) 0.0233 2.5 7.1 4.3 5.05

CM 2

(NLOS) 0.4 0.5 5.5 6.7 10.38

CM 3

(NLOS) 0.0667 2.1 14 7.9 14.18

CM 4

(ENLOS) 0.0667 2.1 24 12 30.1

( sec) T n1 ( sec)n 1( sec) n

Main assumptions on the channel modelA.1) According to J.H.Reed, An introduction to Ultra Wideband Communication

Systems, Prentice Hall 2005 we may approximate each Multiple Cluster SISO channel response

to single cluster one, by considering only the first cluster.A.2) In order to derive the co-decoder block we consider three different

path gains’ ddp: 1) Gaussian 2) Log-Normal 3) Nakagami

A.3) In order to derive the co-decoder block we assume the number V of arrivals and their values to be perfectly estimated

A.4) The path gains are supposed to be spatially uncorrelated A.5) We consider slow-variant fading

0[ ,... ]V

The Co-Decoder block

ML Decoder Block Scheme

Y

rN ( )r t

0{ ,..., }V

Banks of Filters matched to

M-OPPM symbols and their V+1 replicas

1( )y t

( )rNy t

.

DecisionStatistics

Processing and selector of maximum

.

.

NON-COHERENT NON-COHERENT ML ML

SYNCHRONIZERSYNCHRONIZER

1 ( )r t

MLb

Setting of the pulse width TP to mitigate theInter-Pulse-Interference (IPI)

Given the following positions : a) , temporal pulse width (monocycle) used by each transmit antennas b) M, the OPPM constellation cardinality of the symbols used for Space-Time coding of the L-ary

Source Symbols. c) , the exponentially distributed inter-arrivals with arrival mean frequency equal to

Let us set , to meet the following condition:

p

ln(1 )T

M

1i i i

pT (sec.)

pT (sec.)

pT i M for a fraction of the service time, that is

Such choice allows us to mitigate the IPI effect due to the Poisson distributed arrivals

0, no IPI

=0.25, IPI for 25%

of the service time

1(sec )

The outputs of matched filters (matrix representation)

2lgf f

t

N LY H W

N

stands for unitary (MxNt ) Space-Time codeword matrix corresponding to the M-OPPM coded symbols, that is

1[ ( ),...., ( )], 0 1tNl e l e l l L

denotes Unitary (MX1) vector. It is function of the uncoded L-ary source symbol “l”, and biunivocally associated to the M-ary OPPM coded symbol radiated by the i-th transmit antenna

( ) Mie l

H stands for the (Nt X (Nr (V+1)) ) multipath channel matrix

f is the signal to noise ratio per each transmitted bit

W stands for (MxNr (V+1 ) ) Additive Gaussian noise matrix

Nf is the number of frame per each symbol period Ts

Decision Statistics processing and selector of maximum

• The ML Decoder works according to the following criterium:

0 1

ˆ arg max{ }ML ll L

b z

2

0 1 1

0 1 1

0 1 1

( ) ( ) (Gaussian fading )

ln cosh ( ) ( ) ( Log-Normal fading)

ln cosh ( ) ( ) (Nakagami fading)

tr

tr

tr

NNVT

in jn j i

NNVT

il n jn j i

NNVT

in jn j i

y n e l

z y n e l

y n e l

2lge ;nf f c

nt

LN

N

-1

22

1 ;( ) lg

tn

f h f

N

n N L

-1/2

t2h 2

2mN2 2 2 1+

( ) lgnf fn L N

2) Any two distinctive codeword matrices

are composed by 2Nt different columns

Space Time Orthogonal Pulse Position Modulation (STOPPM) codes

Definition 1) The unitary codeword matrices are composed

by M rows and Nt columns. The number M (that is, the OPPM constellation cardinality) is given by product LNt

1 1( ).... ( ) ( ).... ( )t tl mN Ne l e l e m e m e

( / sec/ )B bit Hz 2lg,

( )f p

T

N T

L

L

Es: L=Nt=2

0

10

01

00

00

1

00

00

10

01

M=4

, 0 L -1l l

Property of the STOPPM codes

The spectral efficiency of the STOPPM codes is equal to

The Union-Chenoff upper bound retained STOPPM codes

2

2

20 2

/

2

2

1 ( ) lg

1) 1 ( )1

1 ( ) lg2

r t

fh fV

tE

n fh f

t

N N

Nn L

NP L fading Gaussiano

Nn L

N

2

20 2

4 (2 )2) 1 ( )

( ) 4(lg ( ) )

r tV

tE

n f h

mN

f

N

mNe mP L fading m Nakagami

m LN n

1 1

0 0

13) ,

L L

E lmm l

l m

P PL

2

2 ( , )1

0 1 1

lgexp( ) ( log )

2

ntr

n

cNNV sf f cr j i

lm nn j i t

Le NP E sech C e fading normale

N

( , ) 21 1

2{sec } exp exp 2n ncr j i c

n n rE h C e t C e c t dt

221

lg( , ) ~ ( , ), , f f

n n rt

LNr j i N C

N

“Log-Normal” frustraction integral. It cannot be expressed in closed form .

S.M.Hass, J.H.Shapiro, “Space-Time Codes for Wireless Optical Communications”, Eurasip Journal on Applied Signal Processing, pp. 211-220, no.3, 2002.

Performance of the STOPPM codes

Lg-N fading

Nk- fadingG-fading

Multipath Intense Profile

Nr=3

Nf=6

2 3 4 5 6 7 8 9 1010

-6

10-5

10-4

10-3

10-2

10-1

SNR(dB)

BE

R

Nt=2

Nt=3

Nt=4

CM3’s

1) BER target:

2) Transmit Power: 2.5mW (Typically adopted for outdoor systems)

3) Each parameter of SISO links is according to CM1:

4) The baseband monocycle is equal to the Gaussian pulse second derivative M.Z.Win, R.A.Scholtz, ''Ultra-Wide Banbwidth Time-Hopping Spread Spectrum Impulse Radio for Wireless Multiple Access Communications'', IEEE Tr. on

Comm., vol.48, pp.679-691, Apr.2002.

5) The path loss model is according to the Siviak-Petroff one

K.Siwiak, A.Petroff, ''A Path link model for Ultra Wide Band Pulse Transmissions'', IEEE VTC2001, Rhodes, Greek, May 2001.6) Throughput: 136.0Mbps7) The Log-Normal fading is considered

Coverage Ranges and Troughput (1/2)

610

12.5( sec) , 4.3, 5.05( sec)n T n

p -3dBpT =0.7 nsec, f 2.774GHz, B 2.453GHz

Coverage Ranges and Troughput (2/2)

Nt Nr R(mt)

1 1 12

1 2 26

2 2 32

2 3 47

3 3 55

Table of coverage Ranges reached by the proposed MIMO UWB-IR co-decoder , equipped with the STOPPM codes. Any SISO link is according to CM1.

The IPI effect

2

1 0

IPI

2

1

lg( , ) ( ) ( )

lg( , , ) ( , ) ( , ) ( , , )

tt N Vf f

q n q f pf

Nf

qtf i q n

fn n i n

it

LNy j l h j i d l w j l

N

LNh j f l d T

N

ln(1 )pT

M

CM3’s Multipath Intense ProfileG fading Nt=2, Nr=1, Nf=4

4 6 8 10 12 14 16 1810

-6

10-5

10-4

10-3

10-2

10-1

dB

BE

R

=0=0.65=0.8

Channel Impairments – Spatially correllated Fading (1/2)

1 c 0 0 ............ 0 0

c 1 0 0 ............ 0 0

0 0 1 c ............ 0 0

0 0 c 1 ............ 0 0

...............................

................................

0 0 .....

t rR R

.............. 1 c

0 0 ................... c 1

Spatial Covariance Matrix.

A.Paulray, R.Nabar, D.Gore, Introduction to Space-TimeWireless Communications, Cambridge university Press, 2003.

1/ 2 1/ 2 t w rR H RH

Channel Impariments- Spatially Correlated Fading (2/2)

Lg-N fading

Nt=Nr=2, Nf=12

CM3’s Multipath Intense Profile

Channel Impairments- Cross-Polarization

Nakagami Fading Nt=Nr=2, Nf=15

1 1 .......... 1

1 1 ......... 1

wH=H ⊙X

X

Channel Model

A.Paulray, R.Nabar, D.Gore, Introduction to Space-TimeWireless Communications, Cambridge university Press, 2003.

CM3’s Multipath Intense Profile

Synchronism RecoveryThe ML Synchronizer block

Let us assume that any time arrival estimate is affected by some error , that is

SNR losses due to Asynchronism

[ , ]p pT T ˆ , for any [0,.., ]i i i V

NON-COHERENT NON-COHERENT ML ML

SYNCHRONIZERSYNCHRONIZER

PILOT SIGNALPILOT SIGNAL GENERATOR GENERATOR

FORFOR SYNCHRONISMSYNCHRONISM

RECOVERYRECOVERY

MIMO UWB-IR System Model(with Poisson distributed multipath fading)

1(1)

0

( ) ( )SN

pilot S Wm

x t E s t mT

0, . . .[ ]V

1( )

0

( ) / ( )fN

idata f t f i p

m

UWB IR M OPPM data signal

x t E N p t mT d T

ji0

r t

( ) ( j,i) ( ) ,

1 j N , 1 i N

V

n nn

h t h t

1

rN

j

tN

111( )h t

rN 1( )h t

j1( )h t

t1N ( )h t

r tN N ( )h t

ji0

r t

( ) ( j,i) ( ) ,

1 j N , 1 i N

V

n nn

h t h t

(1)

0

( ,( ) ( ) ( )) j

data signal measured at

j pilo

j t

V

n

han

n

t a

t

en

n

n

h j ir t x t w t

SPACE-TIME CODED SPACE-TIME CODED PACKET TRANSMITTERPACKET TRANSMITTER

ADOPTING OPPMADOPTING OPPMMODULATION FORMAT MODULATION FORMAT

NON-COHERENT NON-COHERENT ML ML

DECODERDECODER

1 0

( ) (( , ) )( )tN

j ji

data signal measured at j thantenna

n

V

n in

h j iy t x w tt

NON Coherent ML Synchronizer- Main Aspects (1/2)

It jointly estimates the number V of arrivals and their values , according to the ML criterium, without any knowledge on the magnitude of the channel coefficients

Such estimation is asymptotically exact

It is pilot-aided

From Cramer-Rao bound point of view, the SIMO version is to prefer to a MIMO version with orthogonal signaling

E.Baccarelli, M.Biagi, C.Pelizzoni, N.Cordeschi, “Multi-Antenna Noncoherent ML Synchronization for UWB-IR faded channels ”, Journal of Communications and Networks (JCN), vol. 8, No.2, pp.194-204, Giugno 2006

0 v,...,

Let us indicate the arrival times’ and channel coefficients vectors, and let be a received signal G.S. representation, then the following joint ML estimation

Joint ML estimation of V and

2

12

21 0 0

1( ); ( ) ( )

Sr NN V

W n jj n mS t

V R s t mT r t dtN

0 0 0... , and (1,1)... ( ,1)....... (1,1)... ( ,1)T T

V r V V rh h h N h h N

ˆ, , ln | , ,arg max0... max

MV MV MVV h p R V h

V N

h

Prop.1Prop.1::

2ˆ, ( );arg max

0...max

MV MVV V R

V N

R

0 v,...,

can be equivalently effected by only estimanting the arrivals times and their number V, that is

with

Properties of the resulting ML equation system :• The i-th equation is function only on the corespondent time

arrival. The (V+1) equations are independent each other• Any solution can be admitted only when :

The ML equations’ system

2

( ); 0i

V R per i V

0 01 1

1 0 0 0 0

ˆ ˆ( ) ( ) ( ) ( ) 0S Sr

T TN NN

W i j W i jj k m

s t kT r t dt s t mT r t dt per i V

ˆi1 01

1

ˆ ˆ ˆ ˆ... 0

ˆ ˆ 0...( 1)

V V

i i PT i V

0,

, 1

0,

ˆ 1,..,

iniz MAX

i iniz i P

R c

T i V

Serial implementation

The expression of Cramer Rao Bound

2

2

1

1ˆ( ) | , per 0,..,

( ,1)r

i i N

S S iS j

E V h i V

N E h j

with

/2

/

0

( ,1)p

p

iT

i VkT

k

eh j

e

+ -

+

Late

LNr

+

(1+Ns)

“early”output

(1)

(2)LOOP

FILTER

Template Signal

Generator

eTw

“late”output

E1

ENr

Early

( ˆ )iv t

+

Tw

( )ˆv t

( )ˆs t

+

L1

Tw

yNr(t)

y1(t)

( ˆ )iv t

MV

X

X

( ˆ )iv t

( )iv tX

yj(t)

dt

dt

blocco Lj

ML Synchronizer

(Early-Late Gate serial version)

Performance of the ML synchronizer

1rN

2rN

4rN

Conclusions The proposed MIMO UWB-IR co-decoder is optimized to work under different path gains pdfs

It works in non-coherent mode

The proposed STOPPM codes can minimize the Union-Chernoff upper bounds

The resulting solution allows to extend the (typically) low coverage of the SISO UWB-IR systems

The proposed ML synchronizer can be simply implemented as serial version of early-late gate.